I also am hoping to populate a text box with the URL of the selected Hyperlink. I think I am along the right path with this code, but I don't know how to complete it:
TextPointer position = RichTextBoxEditor.Selection.Start;
Inline parent = position.Parent as Inline;
foreach (Hyperlink hl in RichTextBoxEditor.Blocks.OfType<Hyperlink>())
{
}